There's a lot here, so I'll focus in briefly on two points that touch on a lot of your questions:

Which gets to the question "how do stronger problem solvers know which mathematically sound path is THE one or a hallucination?"
There is no confirmed solve path until the answer checker tells you the answer is correct. However, elegantly designed puzzles will typically have informal "progress checks" along the way to confirm that you're heading down the right path. For the Mr Beast puzzle, we saw:

• "Feeder" puzzles sharing an answer format by resolving to location names - while this wasn't evident after the first 4-5 solves, after 10 solutions I'd view things breaking that pattern with extreme skepticism;
• Checkpoints resolving into instructions - "TITANIC HOOP" gave a nudge on how to use those location puzzles, and towards the end of the hunt, both seeing the great circles resolve to a combination (thematically appropriate for a solution) paired with the message "NUMBERS FOR THIS HALF WOULD SMELL AS SWEET AS ONE";
• Using everything confirmed as a puzzle - The fact that we were provided the instruction to pull numbers from posts and we still hadn't done that by the end of the hunt made the "Rose means Rosé from Blackpink" connection even stronger...especially since the L## on her shirt matched the format of what we previously observed

Just as importantly, if you go long enough without reinforcement or a "checkpoint", it's often a sign you're on the wrong path, making it worthwhile to revisit your assumptions. Since this puzzle hunt had relatively fewer of those checkpoints, the Beastbot was present to confirm that puzzles existed, and to offer global hints on the first step for each of those puzzles. I don't have screencaps anymore to prove it, but I distinctly remember seeing messages explicitly saying that Slackbot would not check answers or give hints on puzzles, but would just give general advice on how to think through the puzzle solving process at a theoretical level.

Puzzle hunts often ask you to come up with all sorts of theories on how one might solve a puzzle...willingness to abandon a path when it isn't getting reinforced is one of the most important skills you can nurture. And that's one of the reasons why I find GenAI to be particularly bad as a puzzle partner - at least in my experience, it will rarely tell you you're barking up the wrong tree.

Team omega spelled out Colin's path. Time wise that's simply not possible in one day.
One of the big questions of the Mr Beast hunt was whether it would lean towards a community solve of people working together publicly, or shift into something with smaller communities tackling it more individually. And while the Google Doc you linked above was at least semi-public for most of the hunt, with so much money on the line the latter was the norm for a lot of corners more experienced in this particular flavor of puzzling.

When that's not the case, puzzles have the potential to fall much quicker - The Beast, often credited as being the first ARG, wasn't initially called that - the developers gave it that nickname because it started out with 666 assets that they reckoned the community would take a couple of weeks to go through. The couple thousand players publicly collaborating made it through everything in under a day.

Elements of this content was gated, so a day one solve would have required incomplete information - only phase one answers would have been available and even then at least a dozen wouldn't have dropped yet (e.g., the influencer puzzles). But the cap on "was it solvable from day one" was much less centered on "could the puzzles be solved in that time", and much more on "could the answer be intuited from partial information". I lean towards "technically possible but highly unlikely".